Question

If two right triangles ABC and DEF are similar, and the legs of ABC are 3 and 4, the shorter leg DEF is 9, then what is the measure of the hypotenuse of DEF?

Answer 1

By applying the Pythagorean theorem and the scale factor from the similar triangles ABC and DEF, the hypotenuse of triangle DEF is determined to be 15 units long.

Step-by-step explanation:

If two right triangles ABC and DEF are similar, and the legs of ABC are 3 and 4 with the shorter leg of DEF being 9, you can find the measure of the hypotenuse of triangle DEF using the Pythagorean theorem.

• First, determine the ratio of the sides of the similar triangles. Since the shorter leg of DEF (9) is 3 times the shorter leg of ABC (3), we can say that the scale factor is 3.
• Next, since ABC has legs of 3 and 4, the length of the longer leg of DEF would be 4 times the scale factor, which is 4*3=12.
• Finally, apply the Pythagorean theorem: hypotenuse of triangle DEF, c = √(9² + 12²) = √(81 + 144) = √225 = 15.

Thus, the hypotenuse of triangle DEF is 15 units long.